This is the Healthcare Market Specialization, Healthcare Marketplace Overview course. I'm Steve Parente, Professor of Finance and you are watching Module 3.1.2, Utility of Wealth. So a major concept in insurance is utility of wealth, and what this graph that you see is depicting, it's a given individual and their utility, and utility is measured on this y-Axis here. Their wealth is on the left axis and what we see for given individual is that as they get more and more money, they get more happiness or more utility. But the other thing that you see is that this curve will change over time. So if you could see here's the slope for this point, then it levels out, then it levels out even further here. This is known as a diminishing amount of marginal utility, the more wealth you have. And you might have experience this as you grow up in life where if you just get like $10, it's like super awesome but as you get older in life and someone gives you $10, unless you're really, really poor you're like, yeah, thanks. And same thing applies here in terms of what you can do with that money. So for example, what we can see is that when someone goes from 0 wealth to say $3000 a month for wealth, their marginal utility, that is 0 minus 65 is 65, or 65 minus 0, excuse me. And then when their wealth goes from, say $3000 to $6000, their utility goes from 65 to 85, but their marginal utility is no longer 85. It is actually 85- 65, which is 20, and 20 is less than 65, meaning that you are diminishing your utility wealth as you get more dollars. Likewise, if you go to 95, when you're earning say, $9,000 the gap there is only a marginal utility of 10. So, as it decreases. Now, why this is matter? The shape of this curve actually gives us some sense of how we value things at lower levels of income much more so. And what it really shows is that, if you are earning a little less, you really will feel a loss of income more and that can create a sense of which known as risk aversion, we'll talk about in a second. Now, utility wealth is a pretty complex idea, but it's core to the insurance area. And so, what we generally do for utility of wealth is we think about translating utility of wealth into what's this concept, and we're going to draw it as expected utility or E(U). Now, expected utility is essentially an idea, where we're trying to get what the average utility might be for a given set of a population as we go forward. So due to uncertainty people do not know exactly what their utility is going to be from particular action. And then the idea of an expected utility is that, that could be translated if for an average set of outcomes are all possible outcomes that we might see. So how might that actually all come into play? Now, this is kind of a busy graph, but it's really kind of an important concept. This is a graph that will represent one person's sort of choices in terms of what they're looking at. And so, the person we're talking about here is Tania, and Tania is generally a very happy person and she has a choice. At choice one, she will have, well $5,000, which is here and her utility will be 80. And that's the case no matter what. Basically, there's nothing to worry about insurance, just that's just the case. $5,000, boom, she's happy. Now at choice two, things are a little different. Choice two, she actually has an opportunity, to maybe make $9,000 or $3,000, and it is actually something that she's not quite sure which way it's going to go. That's why we have this listed as a range of outcomes. Now, to make this actually work, in terms of why we have a utility of all scheduled weeks. We don't know again, all the possible combinations and so, to actually represent that notion with expected utility again, we look at the average of all the outcomes that are possible. And that's what this straight line represents from 65 to 95. That shows us because of the wealth that she's able to earn, what her full range of outcomes are going to be. But the interesting thing is that, if you actually look then, at that average line and you sort of see where things are. It turns out the utility 80, and you drop it down to, and it maps exactly to that point here, that average line. Her wealth is equal to 6. And one last piece you have to understand is that, if her wealth's equal to 6, and she has to gamble to be able to get that money. It turns out that she might not like that, and she might be figuring that gamble means she might want to have to buy off the risk if you will, the cost of risk, this gets to the concept of insurance. And so, at the end of the day her expected utility from doing this choice is really, even though she might have more money it's going to be 80. And since she's really no better off because of this, she might say, yeah, I'm not really indifferent. I might just go with choice one, because I'm really going to be much better off in terms of my utility, though my wealth might be actually higher. So interesting concept but let me show you one other thing that we hopefully will drive this idea further home. So, this issue of risk aversion is a really again, core concept to insurance, and everybody has their own sense of risk aversion. Also, when we compare risk aversion back to, if you will, a control population of risk neutrality. So risk aversion is defined essentially as the amount that someone is willing to trade off their wealth as their marginal utility diminishes and it might be different for different people. So that curve that we showed you before, notice the curve over here. That curve could be like this, it could be like this, it could be somewhere in between. And what's important about that, is that if that curve really bows up high that means, that if you drop a little bit in your income you're really going to feel it more in utility. And the more you feel it, that's the sense of what you would get for risk aversion. So, going to this notion of actually a person who's completely risk neutral, this is someone who basically has no sense of risk aversion. Otherwise, their curve if they're risk aversed might more look like this. If they're extremely risk aversed and they're worried about losing money, it might look more like here. This person pretty much, you know, you give them a little more money, their margin utility isn't really, it's almost an exact function, their slope's always the same. So you folks might know, folks in life where it's like you give them essentially a bottle of water, the guy smiles really happily at you. You give him a bottle of a really great wine and still just smiles, doesn't really care. You give him like, Johnnie Walker Blue Label, which is a really good Scotch. He's just as happy as he was with that bottle of water. That's essentially another way of saying that no matter, really, how much wealth that person is getting, they're not really feeling that much different. Whereas if someone was a little more risk averse here, the sense of losing something will make them a little more antsy. So the way this translates is that in terms of health care is that if someone is really worried about losing their health, they might be willing to pay a lot of money to make sure that they maintain their health. So how do we reduce this risk issue? What do we do? That's really the concept of insurance, where if you are willing to pay someone a premium to reduce your risks, then it's going to cost you some money. But it means that, if something adverse happens to you, you're not going to be any worse off. Your expected utility is still going to be where your utility would be without the insurance policy. And that will give you a certain level of comfort and granted different people are willing to pay more premium in terms of how much risk they're willing to accept. So, that's probably the best way to mitigate your risk is to buy the insurance policy, another way is to buy protection from the mob, this is our little mob car. But that really is not necessary as a solution, at least not yet in your lives. So this concludes our module on the utility of risk. [BLANK AUDIO]
